An effective cooling of gas-turbine components which come into contact with the hot gas of the turbine, such as rotor blades, stator blades or combustor parts, is an important element for controlling the service life and the performance of the machine. Thus, for example air, which is tapped off at the compressor and guided to the hottest points of the gas turbine, is directed through the rotor and the casing. In this way, hot regions of the rotor and of the casing are also cooled, which particularly in the case of the latest generations of high-performance gas turbines is absolutely necessary for these components for achieving the desired service life. In this sense, the tapped-off air fulfills two tasks: it reduces the metal temperatures in the rotor and casing to an acceptable level and then cools components which are exposed to the hot gas, such as turbine blades and combustor parts. The same also applies to other cooling media such as steam which has to be produced specially for cooling purposes or is tapped off from an already existing steam cycle of a combined cycle power plant or from a separate steam boiler. The tapped-off cooling medium is either lost—in an open cooling system—or is returned to the steam cycle—in a closed cooling cycle, wherein, however, some energy losses typically arise.
When designing cooling systems, it is the aim                to reduce the amount of cooling medium which comes from the compressor, from the steam generator, or from another source for the cooling medium; and        to increase the cooling efficiency of the cooling medium, which for example flows through internal cooling passages.        
As an example for such cooling, a turbine blade 10 is shown in FIG. 1. Sub-figure 1a) shows the longitudinal section through the turbine blade 10 and sub-figure 1b) shows the cross section in the plane A-A from FIG. 1a). The turbine blade 10 has a lower part 13 and a blade airfoil 11 which is connected thereto in the radial direction and terminates in a blade tip 12. The blade airfoil 11 customarily has a leading edge 21, a trailing edge 22, and also a pressure side 24 and a suction side 25 between the two edges. A plurality of cooling passages 14, 15, 16 and 17 extend inside the blade airfoil 11 in the radial direction. A cooling medium from the lower part 13 of the blade enters (arrow) the cooling passage 15 and 16, flows towards the blade tip 12, is deflected there by 180° within the limits of a flow reversal 18, and in the cooling passage 14 flows back towards the lower part 13 of the blade and through small cooling passages to the trailing edge 22. The cooling medium which enters the cooling passage 16 finds its way through passages 19 into the adjacent cooling passage 17, and from there discharges outwards through outlet openings 20, 23 in order to cool the blade, for example in the manner of film cooling, on the outer side.
When designing the thermally loaded component (in this case, the turbine blade), the cooling capacity is customarily intensified by provision being made in the cooling passages for different types of obstacles, or by openings or slots of different configuration being arranged between adjacent cooling passages or opposite walls which are to be cooled. These geometric elements are to create either local turbulences in the flow of cooling medium or to increase convection in a local region in order to increase the heat transfer between a hot internal wall of the component and the colder medium. Even if a highly-complex cooling system is provided inside the component which is to be cooled, which in the case of production can be associated with high costs, certain regions, such as corners inside the component which with regard to effective cooling still constitute a challenge, and which on account of local effects such as oxidation, creep or premature crack development may constitute a service-life problem, still remain.
The cooling system generally comprises one or more inlets for entry of the cooling medium into the hot component, and one or more outlets for discharge of the cooling medium. Depending upon the process of heat transfer between the cooling medium and the hot walls of the component, the cooling system comprises different cavities which are interconnected by means of passages or slots. On account of the different configuration, dimensions, temperatures and pressures in these cavities and passages, different acoustic resonances occur in the cooling system. In general, each cavity and each passage has a different acoustic resonance. When designing the cooling system, attention is paid to keeping the Mach numbers in the flow of the cooling medium through the cooling system within specific upper and lower limits in order to avoid flow separation and regions of poorer heat transfer which are associated therewith.